Discrete Painlev\'e equations and random matrix averages
Forrester, P. J. ; Witte, N. S.
arXiv, 0304020 / Harvested from arXiv
Text on arXiv
The $\tau$-function theory of Painlev\'e systems is used to derive recurrences in the rank $n$ of certain random matrix averages over U(n). These recurrences involve auxilary quantities which satisfy discrete Painlev\'e equations. The random matrix averages include cases which can be interpreted as eigenvalue distributions at the hard edge and in the bulk of matrix ensembles with unitary symmetry. The recurrences are illustrated by computing the value of a sequence of these distributions as $n$ varies, and demonstrating convergence to the value of the appropriate limiting distribution.
Publié le : 2003-04-13
Classification:  Mathematical Physics 
@article{0304020,
     author = {Forrester, P. J. and Witte, N. S.},
     title = {Discrete Painlev\'e equations and random matrix averages},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0304020}
}

Forrester, P. J.; Witte, N. S. Discrete Painlev\'e equations and random matrix averages. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0304020/